With the greater number of high quality 6.5mm heavy bullets, I'd pick the 6.5-06 over the .270. It's barrel life for tack driving accuracy (that is, starting out at 1/4 MOA biggest groups at 100 yards) will be about 800 rounds compared to 1000 for the .270, it may be worth it. Both are overbore cartridges therefore, barrel life will be short.
US Navy Distinguished Marksman Badge 153
Former US Navy & Palma Rifle Team Member
NRA High Power Master & Long Range High Master
NRA Smallbore Prone Master